Some central limit theorems for Markov paths and some properties of Gaussian random fields
type: Item
instance of: scholarly article
title: Some central limit theorems for Markov paths and some properties of Gaussian random fields
zbMATH Open document ID: 0615.60037
DOI: 10.1016/0304-4149(87)90012-3
author: Robert J. Adler
author: Raisa Epstein Feldman
published in: Stochastic Processes and their Applications
publication date: 1987-01-01T00:00:00Z
review text: Our primary aim is to ''build'' versions of generalised Gaussian processes from simple, elementary components in such a way that as many as possible of the esoteric properties of these elusive objects become intuitive. For generalised Gaussian processes, or fields, indexed by smooth functions or measures on \({\mathbb{R}}^ d\), our building blocks will be simple Markov processes whose state space is \({\mathbb{R}}^ d\). Roughly speaking, by summing functions of the local times of the Markov processes we shall, via a central limit theorem type of result, obtain the Gaussian field. This central limit result, together with related results indicating how additive functionals of the Markov processes generate additive functionals of the fields, yield considerable insight into properties of generalized Gaussian processes such as Markovianess, self-similarity, ''locality'' of functionals, etc. Although the paper is comprised primarily of new results, and despite the fact that the subject matter is somewhat esoteric, our aims are primarily didactic and expository - we want to try to initiate the uninitiated into some of the mysteries of generalised processes via an easily understood model.
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60G20
Mathematics Subject Classification ID: 81T08
zbMATH DE Number: 3996764
zbMATH Keywords: Euclidean quantum fields
zbMATH Keywords: central limit theorem
zbMATH Keywords: Markov property for fields
zbMATH Keywords: Wick powers
zbMATH Keywords: Gaussian field
zbMATH Keywords: additive functionals
MaRDI profile type: Publication
full work available at URL: 0304-4149(87)90012-3
OpenAlex ID: W2050018531
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description: scientific article; zbMATH DE number 3996764